There are two mobile operators in Qatar:
Vodafone
Vodafone is number 2 in Qatar, but if you’re mainly in the centers it’s a slightly cheaper alternative. 4G/LTE is available in Doha, Pearl and West Bay
English website: http://www.vodafone.qa/en
Ooredoo
Ooredoo (formerly Qtel) is the market leader in Qatar with more than 2/3 of all customers in the country. It has the best coverage and speed in the country
English website: https://www.ooredoo.qa/
Censorship in Qatar
Qatar also “filters” online censorship of pornography, political criticism of the Gulf states, gay and lesbian content, sexual health resources, dating and escort services, and privacy and bypass tools. Users complain that obscene or offensive sites are also blocked. That way you can install a proxy or VPN before bypassing. Filtering in Qatar is relatively transparent as it shows the blocked site instead. Internet is uncensored at least in some international hotels.